In a typical structure, there are many vibration modes over a wide range of frequencies. One important goal of modal analysis is to identify and properly characterize each of these modes. The bandwidths of the various modes are governed by two parameters, one being the natural frequency itself and the other being the quality factor Q. If the Q value is fixed, then bandwidth is only proportional to the natural frequency. For example, with a similar Q value, the bandwidth of a resonance at 1000 Hz frequency can be as wide as a few dozen up to a hundred Hertz, while for a resonance in the 1.0 to 10 Hz frequency range, the bandwidth can be as narrow as less than one Hertz. Because of this, most characteristics of a dynamic mechanical system are better described using different resolutions in the frequency axis, needing higher analysis frequency resolution for lower natural frequency modes.
In a multi-input multi-output (MIMO) test, multiple exciters and multiple measurement sensors are configured. Excitation signals will have a broadband excitation energy and usually have a random nature, e.g. random, pseudo-random, burst random, chirp, periodic random, white noise, pink noise etc. A first requirement for modal analysis of MIMO test results is to measure the frequency response functions of the structure under test. When a traditional Fast Fourier Transform (FFT) method is used, the frequency resolution is always uniform across the whole frequency range covered by the transformation. Assuming, for a typical setup, that the test goes up to 2000 Hz vibration frequency, 2048 points of time block, and 800 frequency lines of FFT spectrum are sampled at a rate of 5120 Hz, the FFT method will provide a resolution for the frequency response function of (2000/800) Hz=2.5 Hz. Due to the nature of structural vibrations, such resolution, while sufficient for higher frequency modes, is not suitable for any modes of less than about 100 Hz.
If, instead, we increase the resolution tenfold to 0.25 Hz to be able to properly characterize low frequency modes, then the data capture size to perform the FFT must also increase tenfold. Considering that in a typical modal analysis project that hundreds or thousands of sensor signals are acquired, increasing the already large size of the data array to be stored by an order of magnitude is not at all desirable, particularly since much of that data is simply wasted at the higher frequency modes. Not only does the increase of FFT size create a storage issue for the data, but since time for data capture is proportional to its size, the testing duration will also need to increase tenfold. The time needed for FFT processing of the extra data will likewise increase. Still further, unless we adopt some different excitation technology, there may not be enough excitation energy in the low frequency band to generate a usable response, and the strategy of increasing FFT size will still produce unsatisfactory results.
Several different methods have been chosen to deal with these problems. One common approach is to conduct the modal tests multiple times at different frequency ranges. For example, in one round of testing, the excitation frequency range could be set to 2000 Hz and all resonance modes at or above 100 Hz identified, and in another round of testing, the excitation frequency range could then be set to 100 Hz to identify the low frequency resonance modes. When the frequency range is set differently, the energy of the excitation signals will adjust accordingly, so the same FFT resolution can be used while still obtaining good accuracy for the frequency response function at all tested frequencies. However, each modal test is already a very time-consuming process. Due to the limited number of sensors and input channels usually available, a typical test needing 200 measurement points (i.e. sensor locations with directions) but using only eight sensors will conduct 25 measurements, moving the sensor locations 25 times, and take a few days to finish. Having to redo the test twice (or multiple times) for different frequency ranges will multiply the testing time. Additionally, testing data management becomes more complex, because test results for different frequency ranges are not stored and presented with integration.
Another common approach is to use either a swept or step sine excitation in place of random excitation. A sine test allows the excitation of a structure to sequentially concentrate upon one frequency at a time. Swept sine uses a continuously changing frequency, while in a stepped sine test the excitation dwells for a time at each frequency then steps or increments to the next frequency. The main disadvantage with either of these sine methods is that it takes even longer time, each sweep or stepping through of a test frequency range taking hours to finish, especially at low frequency where the sweeping is slower or the step increments are smaller. Another disadvantage is that structures often exhibit complex nonlinear behaviors (mode coupling) when many modes of vibration occurring at the same time interfere with each other. Because the sine test sequentially excites only one frequency at a time, it cannot adequately reproduce the actual environment where structures are simultaneously excited across a wide band of frequencies.
The discussion above describes the need to have different analysis frequency resolution to analyze the spectral data over the frequency range of interest. In fact, there is also a need to have more than one exciter to generate the vibration with different energy distribution at different frequency range. For example, for a large aircraft structure testing, it may be desired to use a hydraulic shaker to generate very large displacement in the frequency range of less than 10 Hz, while an electro-dynamic exciter is used to generate the vibration above 10 Hz. When multiple shakers are used, the shape of output force spectra, or summation of them, should be controlled. The previous techniques using multi-exciters did not address the demand of using different frequency resolution to analyze the data.